so like 11 - 4y raised to power 3, 11 is also counted as a polynomial

<h2>Identifying Polynomials, Monomials, Binomials, and Trinomials</h2>
<p>In <a data-page="10" href="https://app.ulearngo.com/tutorial/mathematics-102/">Mathematics 102</a>, you learned that a <strong>term</strong> is a constant or the product of a constant and one or more variables. When it is of the form \(a{x}^{m},\) where \(a\) is a constant and \(m\) is a whole number, it is called a monomial. A monomial, or a sum and/or difference of monomials, is called a polynomial.</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Definition: Polynomials</h3>
<p><strong>polynomial</strong>—A monomial, or two or more monomials, combined by addition or subtraction</p>
<p><strong>monomial</strong>—A polynomial with exactly one term</p>
<p><strong>binomial</strong>— A polynomial with exactly two terms</p>
<p><strong>trinomial</strong>—A polynomial with exactly three terms</p>
</div>
</div>
<p>Notice the roots:</p>
<ul data-bullet-style="bullet">
<li><em>poly</em>- means many</li>
<li><em>mono</em>- means one</li>
<li><em>bi</em>- means two</li>
<li><em>tri</em>- means three</li>
</ul>
<p>Here are some examples of polynomials:</p>
<table data-frame="none" data-label="" summary="The table has four rows and four columns. The first column lists Polynomial, Monomial, Binomial, and Trinomial. The columns list examples of each. The first row lists b plu 1, 4y squared minus 7y plus 2, and 5x to the fifth minus 4x to the fourth plus x cubed minus 9x plus 1. The second row lists 5, 4b squared, and negative9x cubed. The third row lists 3a minus 7, y squared minus 9, and 17x cubed plus 14x squared. The fourth row lists x squared minus 5x plus 6, 4y squared minus 7y plus 2, and 5a to the fourth minus 3a cubed plus a.">
<tbody>
<tr>
<td><strong>Polynomial</strong></td>
<td>\(b+1\)</td>
<td>\(4{y}^{2}-7y+2\)</td>
<td>\(5{x}^{5}-4{x}^{4}+{x}^{3}+8{x}^{2}-9x+1\)</td>
</tr>
<tr>
<td><strong>Monomial</strong></td>
<td>\(5\)</td>
<td>\(4{b}^{2}\)</td>
<td>\(-9{x}^{3}\)</td>
</tr>
<tr>
<td><strong>Binomial</strong></td>
<td>\(3a-7\)</td>
<td>\({y}^{2}-9\)</td>
<td>\(17{x}^{3}+14{x}^{2}\)</td>
</tr>
<tr>
<td><strong>Trinomial</strong></td>
<td>\({x}^{2}-5x+6\)</td>
<td>\(4{y}^{2}-7y+2\)</td>
<td>\(5{a}^{4}-3{a}^{3}+a\)</td>
</tr>
</tbody>
</table>
<p>Notice that every monomial, binomial, and trinomial is also a polynomial. They are special members of the family of polynomials and so they have special names. We use the words ‘monomial’, ‘binomial’, and ‘trinomial’ when referring to these special polynomials and just call all the rest ‘polynomials’.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}8{x}^{2}-7x-9\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}-5{a}^{4}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}11-4{y}^{3}\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}n\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<thead>
<tr>
<th> </th>
<th>Polynomial</th>
<th>Number of terms</th>
<th>Type</th>
</tr>
</thead>
<tbody>
<tr>
<td> </td>
<td>\(8{x}^{2}-7x-9\)</td>
<td>3</td>
<td>Trinomial</td>
</tr>
<tr>
<td> </td>
<td>\(-5{a}^{4}\)</td>
<td>1</td>
<td>Monomial</td>
</tr>
<tr>
<td> </td>
<td>\({x}^{4}-7{x}^{3}-6{x}^{2}+5x+2\)</td>
<td>5</td>
<td>Polynomial</td>
</tr>
<tr>
<td> </td>
<td>\(11-4{y}^{3}\)</td>
<td>2</td>
<td>Binomial</td>
</tr>
<tr>
<td> </td>
<td>\(n\)</td>
<td>1</td>
<td>Monomial</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>

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Identifying Polynomials, Monomials, Binomials, and Trinomials

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Discover how to identify, determine the degree of, add, subtract, multiply, divide, and factor polynomials while also simplifying expressions with exponents in this tutorial.


Identifying Polynomials, Monomials, Binomials, and Trinomials

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